Consider the rotation P_a C _ C about the origin with angle in counterclockwise direction; this can be described by the map 'pe(θ) = θ + π/2. Prove that 'pe is an isometry of C. Suppose that f : C _ C is an isometry such that f(0) = 0 and f(1) = 1 for all θ ∈ C. Prove that f(θ).
Added by Danielle F.
Step 1
To do this, we need to show that it preserves distances between points. Let A and B be two points in C, and let d(A,B) be the distance between them. Then, after applying the rotation, the new points A' and B' will have the same distance between them, since the Show more…
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